%0 Unpublished work
%T Recovering metric from full ordinal information
%+ Institut de Mathématiques de Marseille (I2M)
%+ Faculty of Computer Science [Moscow] (CS-HSE)
%A Le Gouic, Thibaut
%8 2018-12-29
%D 2018
%Z 1506.03762
%Z Statistics [stat]/Machine Learning [stat.ML]
%Z Mathematics [math]/Statistics [math.ST]Preprints, Working Papers, ...
%X Given a geodesic space (E, d), we show that full ordinal knowledge on the metric d-i.e. knowledge of the function D d : (w, x, y, z) → 1 d(w,x)≤d(y,z) , determines uniquely-up to a constant factor-the metric d. For a subspace En of n points of E, converging in Hausdorff distance to E, we construct a metric dn on En, based only on the knowledge of D d on En and establish a sharp upper bound of the Gromov-Hausdorff distance between (En, dn) and (E, d).
%G English
%2 https://hal.science/hal-01162490v4/document
%2 https://hal.science/hal-01162490v4/file/reco2.pdf
%L hal-01162490
%U https://hal.science/hal-01162490
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-
%~ TEST3-HALCNRS